Do start with the simple things. How much fuel in the tank, and is it low enough that the reserve setting is required?
The stock tank has a great fuel filter in the tank right above fuel valve. When in good condition, there is no need for an inline filter.
So, why do you have an external and why is it collecting stuff?
Next step would be to verify gas get to all the carb bowls. There is a drain tube at the bottom of each bowl and a screw just above it that allows the carb bowl to drain into that tube.
You can do three things with this arrangement. One is to see if fuel drains from each bowl. Two is see what comes out beside clean gas. And three, is to see/measure how much volume of gas comes from each carb bowl.
Once you have verified that all carbs get an equal amount of clean gas, you can address choke operation by verifying the the choke cable pull the linkage to its fullest extent. There is some adjustment to this cable at the clamp to achieve this.
The above addressed, the engine will either start or attempt to start. In either case, a wet rag applied to the header pipes ought to tell you which pipes are getting hot. I do this with my fingers in a "flash touch" maneuver, as touching a hot surface quickly will not burn you, but you will still get a sense for heat present. Hold your hand on a hot header pipe and it WILL burn you before your brain can register extreme and damaging heat.
The pilot jets are only about 0.016 inch in diameter and therefore clog pretty easily with foreign debris. Cold head pipes often indicate a clogged pilot jet. Hope this isn't the case, because it is a challenge to yank them from the carb bodies for cleaning, and doubly so to clean them without removing the carbs from the bike. The latter often leads to rubber coupler damage, and it is VERY difficult to obtain a replacement set of those.
Do the simple things first and report your findings. We can then advise next steps.
Another thing you can do is to pull the spark plugs and note their tip condition and deposit patterns. This is your "window" for combustion conditions. And, they can tell you what issues are cause for not running as expected. Naturally they should all look exactly the same as each other for them all to work the same.
Cheers,
